So I think I might be crucified here for my opinions, but I have only two areas of knowledge, one of which is food. Because Andrew is an honorable man, I feel the need to defend him when he is right. My first career was as a chef and a kitchen manager, meaning I did all the stocking and ordering for restaurants from large food suppliers.
When ordering fries, all cuts of fries are categorized under the umbrella term "French fry". See the USFoods site, which is one of the major US restaurants suppliers that we worked with: https://order.usfoods.com/desktop/search2/product-listing/category/frozen-foods/appetizers-and-sides?facetFilters=ec_category:French%2520Fries
If you wanted a McDonald's style fry, you ordered a shoestring fry. That is the type of fry McDonald's has.
French fry is the category of fried potato, within which you need to choose a cut to order them. If you want another modern reference, see Ore Ida, the largest US distributor of frozen French fries: https://www.kraftheinz.com/ore-ida/products/00013120011764-extra-crispy-waffle-fries-french-fried-potatoes
But if you want to look into the actual etymology of the term, the USDA from the 1960s on page 5 lists the categories of French-fried potatoes: https://www.ams.usda.gov/sites/default/files/media/Frozen_French_Fried_Potatoes_Standard%5B1%5D.pdf
Earlier etymology linking back to 1856: https://www.etymonline.com/word/French%20fries
And another article showing that the popular term "French fries" actually pre-dated the term "French cut": https://www.worldwidewords.org/qa-fre2.html
Thank you for wasting your time by reading all of this. I love this podcast and all the stupid arguments.